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Quantum Demiric-Selçuk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions

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Security and Cryptography for Networks (SCN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11035))

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Abstract

This paper shows that quantum computers can significantly speed-up a type of meet-in-the-middle attacks initiated by Demiric and Selçuk (DS-MITM attacks), which is currently one of the most powerful cryptanalytic approaches in the classical setting against symmetric-key schemes. The quantum DS-MITM attacks are demonstrated against 6 rounds of the generic Feistel construction supporting an n-bit key and an n-bit block, which was attacked by Guo et al. in the classical setting with data, time, and memory complexities of \(O(2^{3n/4})\). The complexities of our quantum attacks depend on the adversary’s model. When the adversary has an access to quantum computers for offline computations but online queries are made in a classical manner, the attack complexities become \(\tilde{O}(2^{n/2})\), which significantly improves the classical attack. The attack is then extended to the case that the adversary can make superposition queries. The attack is based on 3-round distinguishers with Simon’s algorithm and then appends 3 rounds for key recovery. This can be solved by applying the combination of Simon’s and Grover’s algorithms recently proposed by Leander and May.

Due to space limitations, some details and proofs are left to the full paper [HS17].

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Notes

  1. 1.

    Dong and Wang [DW17] independently pointed out the combination of the 3-round distinguisher [KM10] and key recovery attack [LM17].

  2. 2.

    Since any Q1 attack can be trivially converted to a Q2 attack by regarding quantum oracles as classical oracles, we can construct a Q2 attack with \(\max (T, D, M, N)\,=\,N^{1/2} \ll N^{3/4}\) from the best Q1 attack. However, such a Q2 attack requires time \(T=N\) in the case that only \(O(\log N)\) qubits are available.

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Authors and Affiliations

  1. NTT Secure Platform Laboratories, 3-9-11, Midori-cho Musashino-shi, Tokyo, 180-8585, Japan

    Akinori Hosoyamada & Yu Sasaki

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  1. Akinori Hosoyamada
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  2. Yu Sasaki
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Correspondence to Akinori Hosoyamada .

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  1. University of Catania, Catania, Italy

    Dario Catalano

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Hosoyamada, A., Sasaki, Y. (2018). Quantum Demiric-Selçuk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_21

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  • DOI: https://doi.org/10.1007/978-3-319-98113-0_21

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